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Theses and Dissertations 1. Thesis and Dissertation Collection, all items
1987
Models for conducting economic analysis of
alternative fuel vehicles.
Grenier, Danny R.
http://ndl.handle.net/10945/22371
This publication is a work of the U.S. Government as defined in Title 17, United
States Code, Section 101. Copyright protection is not available for this work in the
United States.
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DUDLEY KNOX LIBRARY
WAVAL POSTGRADTATE SCHOOL
MONTHREY, CA LIVCGRNLTA 93945-8008
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
MODELS CR CONDUCTING ECONOMIC ANALYSIS
OF Afar ESP Uri aC
by
Danny R. Grenier
June 1987
Thesis Advisor: Dan C. Boger
Approved for public release; distribution is unlimited
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OFFICE SYMBOL 7a NAME OF MONITORING ORGANIZATION
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Nava PO graduate Schoo Gogews4 NawalmPestciaduace School
6c ADDRESS (City State, and ZIP Code) 7b AOORESS (City, State, and ZIP Code)
6b
6a NAME OF PERFORMING ORGANIZATION
Momeerey, California 93943-5000 Monterey, California 93943-5000
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MODELS FOR CONDUCTING ECONOMIC ANALYSIS OF ALTERNATIVE FUEL VEHICLES
‘2 PERSONAL AUTHOR(S)
aC Nanny R
"3g TYPE OF REPORT . 135 TIME COVEREO 14 OF PORT (Year Month Day) 1S PAGE COLNT
Master's Thesis FROM TO 19875 June d 74
"6 SUPPLEMENTARY NOTATION
GOSATILGODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by biock number)
FELD Aleernaeivecenuecls- se llectriec Vehicles;
a ae Dual Fuel Vehicles; CNG Vehicles
a
"9 ABSTRACT (Continue on reverse if necessary and identify by block number)
The present status of alternative fuel vehicles, specifically electric-
powered and compressed natural gas-powered vehicles is summarized. Spee Time
advantages and disadvantages of each vehicle type, in comparison to the
gasoline-powered vehicle, are reviewed. A life cycle cost model is formu-
lated for each vehicle type. An integer linear program is derived and
explained as a means of determining the optimal mix of vehicles for a
command's transportation fleet. The models are tested by running several
test cases using data from the Naval Postgraduate School transportation
office.
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1
Approved for public release; distribution is unlimited
Models for Conducting Economic Analysis of
Alternative Fuel Vehicles
by
Danny R. Grenier
Lieutenant, Supply Corps, United States Navy
B.S., Radford College, 377
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN MANAGEMENT
from the
NAVAL POSTGRADUATE SCHOOL
June 1987
CC
ABSTRACT
The present status of alternative fuel vehicles,
specifically electric-powered and compressed natural gas-
powered vehicles is summarized. Specific advantages and
disadvantages of each vehicle type, in comparison to the
gasoline-powered vehicle, are reviewed. A life cycle cost
model is formulated for each vehicle type. An integer
linear program is derived and explained as a means of
determining the optimal mix of vehicles for a command's
transportation fleet. The models are tested by running
several test cases using data from the Naval Postgraduate
School transportation office.
dels
TABBED Or CONTENTS
INTRODUCTION ------------------------ +--+
A. PROBLEM STATEMENT ----------------------~~~~~ ~
B. OBJECTIVE --------------------------~
Cc: ALTERNATIVES ----------------~----- +--+
D. ALTERNATIVE SELECTION CRITERIA —-———— ==
E. MEASURES OF EFFECTIVENESS —————_ =e
F. ASSUMPTIONS -------------------------~-+-
G. RESEARCH METHODS ----------------------~~~~ —
H. SUMMARY ----------------------------~
ALTERNATIVES ---------------------- — +
A. ELECTRIC=-POWERED VEHICLES ---------------~~-——
1. Background ------------------- ---------+--
2. Vehicle Description ---------------------
a. The Battery -------------------------
b. The Controller =-—--====—-=.=.-—]]-]2.. 22
Ss The Motor --------------------~---~~-~-~-—
d. The Transmission -<-<----------<------—
e. The Differential -------------------~-
3. Advantages of Electric-Powered Vehicles -
4. Disadvantages of Electric-Powered
Vehicles --------------------------~+~-~-~~
5. Electric-Powered Vehicle Performance
Data ----------------- - - - - - - - - - -
6. Electric-Powered Vehicle Cost Data ------
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Te
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Ls
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26
26
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mil. THE
IV. THE
APPENDIX:
COMPRESSED NATURAL GAS-POWERED VEHICLES -----
1. Background ----------------9 999-52 -------
2. Vehicle Description ---------------------
3. Advantages of Compressed Natural Gas
Vehicles --------------------------------
4. Disadvantages of Compressed Natural
Gas Vehicles ----------------------------
5. Compressed Natural Gas Vehicle
Performance Data ------------------------
6. Compressed Natural Gas Vehicle
Cost Data -------------------------------
LIFE CYCLE COST MODEL -----------------------
LIFE CYCLE COST COMPONENTS ------------------
LIFE CYCLE COST FORMULA ---------------------
CASOMNE-—POWERED VEHICLE Etat CYCLE COST ==--
Preece POVERE Dev EneeCEE LiFe -CyYCchn coOsr ——-——
COMPRESSED NATURAL GAS-POWERED VEHICLE
LIFE CYCLE COST -----------------------------
LINEAR PROGRAMMING MODEL --------------------
FIXED CHARGE INTEGER LINEAR PROGRAM MODEL ---
SUMMARY AND CONCLUSIONS ---------------------
VERCLE DLiRE CYGCERE COST €COMeEUrALIONS ==--=-=--
LIST OF REFERENCES errr rrr rrr tt tr strstr tert ttc ccc cccscccc
INITIAL DISTRIBUTION LIST cerrrrrr rr rrr rrrrrrrrrssrscrc---
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ive INTRODUCETON
Today's military managers must contend with decreasing
budgets while mission requirements continue to expand. In
order to meet these expanding requirements, military
managers must conserve the scarce financial resources
available to them.
The Public Works Center Transportation Office is
required to provide vehicles for the transportation
requirements oof the commands it supports. These
transportation requirements run the gamut from maintenance
vehicles to passenger sedans to passenger buses. The means
of propulsion for all of these vehicles is usually the
internal combustion engine with gasoline as the fuel source.
Recent history has shown the price of gasoline to be
somewhat less than _ stable. This instability can be a
financial manager's nightmare. Departmental budgets are
forecasts or predictions of what funds the department
believes it will require for some future period. In the
government, this future period can be more than a year away.
Thus, the budget the transportation manager submits today
can be drastically affected by an increase in the price of
gasoline tomorrow. What the transportation officer desires
is a fuel source which is cost effective and stable in
price.
Two alternative fuel source vehicles that have generated
interest within the transportation industry are electric-
powered vehicles and compressed lgvstieblersi IL gas-powered
vehicles.
This thesis looks at these two alternative fuel vehicles
and compares them to the present baseline of the gasoline-
powered internal combustion engine vehicles. In order to
Simplify matters, this thesis will only deal with sedans,
vans, and light trucks.
Formulas for computing the life cycle costs of the
vehicles are derived in the thesis. After determining the
life cycle costs of the various types of vehicles, the
transportation manager must decide what mix of the various
types of vehicles would allow him to meet his operational
requirements at the lowest cost. In other words, what mix
allows him to optimize his transportation budget?
The thesis explains the use of a fixed charge linear
program to obtain the optimal mix of vehicles. Linear
programming is an operations research tool which is used to
determine the optimal allocation of limited resources, in
this case, the transportation budget. fieeaoing lanear
programming, the manager can subject the results’ to
sensitivity analysis which allows the manager to test the
optimal solution by changing the various constraints such as
the funding level or various cost elements (i.e., fuel cost,
maintenance cost, operating cost) and observing the effects
on the optimal solution.
we PROBLEM STATEMENT
The instability of the cost of gasoline has stimulated
an interest in alternative fuel vehicles. A means to
compute the life cycle costs of the various types of
vehicles is required. Having determined the life cycle
costs of the various vehicle types, the transportation
manager requires a means of determining the optimal mix of
the vehicle types based on his budget constraint and mission
requirements.
Bi OBUECTIVE
The research objective is to derive a procedure for
computing the various vehicle life cycle costs, then use
these life cycle costs to determine the optimal mix of
vehicle types. The underlying objectives are:
1. Present an overview of the present state of the art of
the electric-powered vehicle industry and the
compressed natural gas-powered vehicle industry. This
overview will include an assessment of the operational
capabilities of both the electric-powered vehicle and
the compressed natural gas-powered vehicle.
2. Develop a model for determining the life cycle costs
of the various vehicle types.
3. Develop a fixed charge linear program for determining
the optimal mix for a typical Public Works Center
transportation fleet.
C. ALTERNATIVES
The - alternatives to the gasoline-powered internal
combustion engine vehicle that are considered are the
electric-powered vehicle and the compressed natural gas-
powered vehicle.
The electric-powered vehicle has been tested extensively
by large companies and the United States Postal Service.
While it is not a widely used vehicle in the United States,
it is quite popular overseas. There are various limitations
on the use of the electric vehicle due to its limited range
and cruising speed.
The electric vehicle must be recharged daily. A few
models of electric vehicles are equipped with an onboard
charging unit but this is the exception rather than the
rule. As such, the electric vehicle is usually required to
return to the charging unit each night. This makes the
electric vehicle impractical for extended trips.
Another limitation on the use of the electric vehicle is
the cruising speed attainable by the vehicle. While some
vehicles are able to attain speeds of over 55 miles per
hour, this, again, is the exception rather than the rule. A
drawback of attaining high speeds in an electric vehicle is
that the range of the vehicle is drastically decreased with
an increase in speed. Most electric vehicles are designed
to operate most efficiently at speeds of up to 35 miles per
MOUTr .
The compressed natural gas-powered vehicle has been used
extensively by natural gas utility companies in the United
States. Much like the electric vehicle, it enjoys more
popularity overseas than in the United States. The
compressed natural gas-powered vehicle that is most popular
is actually a conversion of the gasoline-powered internal
combustion engine vehicle. The conversion process allows
the vehicle to operate using either compressed natural gas
or gasoline. Due to this ability to use two fuels, it is
termed a dual fuel vehicle.
Due to this dual fuel capability, the compressed natural
gas vehicle does not have the range limitations that the
electric vehicle carries. If a compressed natural gas
vehicle is required to operate in an area where natural gas
refueling equipment is not available, a simple turn of a
valve will switch the vehicle from natural gas fuel to
gasoline.
The primary limitation caused by the compressed natural
gas conversion of the gasoline internal combustion engine
vehicle is a loss of cargo space due to installation of the
compressed natural gas cylinders.
The electric-powered vehicles and the compressed natural
gas-powered vehicles will be judged against the baseline of
the gasoline-powered internal combustion engine vehicle.
Due to the widespread use of the gasoline vehicle and its
operational capabilities, there are few limitations on the
10
vehicle type. Range is unlimited due to the many gasoline
stations in the United States and overseas. Nearly all
gasoline-powered vehicles can easily attain the national
speed limit of 55 miles per hour.
Due to the unlimited range and the high cruising speed
attainable by gasoline-powered vehicles, these vehicles are
considered high performance vehicles. In contrast, low
performance vehicles would be characterized by cruising
speeds of less than 55 miles per hour and reduced range.
For the purpose of this thesis, the optimal vehicle is
the vehicle which meets the minimum mission requirements
placed upon it at the lowest life cycle cost.
D. ALTERNATIVE SELECTION CRITERIA
The two keys to determining the optimal vehicle for a
particular task are:
1. Determining the requirements that will be placed upon
the vehicle.
2. Determining which vehicle type can meet the minimum
requirements of the task at the lowest life cycle
cost.
These two keys require the Public Works Center
transportation officer to first determine the types of
requirements that are placed on his vehicle fleet. These
requirements are usually in terms of range, cruising speed,
and load.
Once the transportation officer has determined how many
high performance vehicles and low performance vehicles are
Itt
required to meet the requirements placed on his department,
he can then look at meeting these requirements with the
lowest life cycle cost vehicle type.
E. MEASURES OF EFFECTIVENESS
The following measures of effectiveness are used to
determine whether a vehicle type is classified as high
performance or low performance.
1. Range--Range is defined as the distance a vehicle can
travel between refuelings. For the purposes of this
thesis, the terms refueling and recharging are
synonymous. A high performance vehicle is capable of
unlimited range. A low performance vehicle's range is
limited by the location of its refueling station.
(homebase).
2. Maximum cruising speed--The maximum cruising speed is
defined as the maximum speed a vehicle must be able to
attain and travel at for an extended period of time.
This is not to be confused with the maximum speed
attainable by a vehicle which is the highest speed a
vehicle can attain but can't hold for an extended
period of time without risking damage to the vehicle.
A high performance vehicle 1s capable of attaining a
maximum cruising speed of 55 miles per hour, the
national speed limit. A low performance vehicle's
maximum cruising speed is less than 55 miles per hour.
The load capabilities of the vehicle types are more a
function of the individual vehicle design rather than the
vehicle type and as such load capability will not be used as
a measure ort GlEeCCEivVeness.
F. ASSUMPTIONS
In order to conduct this study, certain assumptions have
been made. Those assumptions are:
1. The number of vehicles needed to meet the requirements
placed upon the Public Works Center transportation
12
office will not change due to the type of vehicle
chosen to meet the requirement. The number of
vehicles in the transportation office fleet will
remain constant.
2. Future requirements placed upon the vehicles will be
consistent with past requirements. Required range and
maximum cruising speed for a particular vehicle will
not change in the near future.
3. Initial procurement cost, maintenance cost per mile,
operating cost per mile, and fuel efficiency ratings
are equal for each vehicle in a particular vehicle
type (i.e., gasoline-powered, electric-powered, or
natural gas-powered).
4. All vehicles will be procured at the same time, Year
1, and disposed of at the end of their useful life.
5. All cost data used in the life cycle cost model will
be in 1986 dollars. Cost figures from research
Material will be adjusted to reflect value in 1986
dollars. Adjustments will be made in accordance with
Table 1, which lists the Consumer Price Indices for
gasoline, natural gas, electricity, new automobiles,
and the general price index of all items.
fee RESEARCH METHODS
A literature search was conducted to obtain a
bibliography of articles, studies, and research papers
written on the current state of the art of electric-powered
vehicles and compressed natural gas-powered vehicles. The
search included articles on the claimed performance
capabilities of the alternative fuel vehicles as well as
actual usSe studies done on the vehicles. These performance
capabilities were used to classify the alternative fuel
vehicle types as either high or low performance vehicles.
13
Year
Lo ZO
uo7
ow Z
L9o73
1974
LoS
L376
oa
L378
Low S
1980
19'S.
£982
£933
1984
1985
1986
Note:
Sources:
Gasoline
105.
106.
107.
ior.
os
oe
ee
Loor
T2O.
260.
Oo
410.
369%.
Beh Oe
O87 O%.
370%
202.
mM ON W WY O FP WwW NY OO WO OO FF HW WwW DW
CONSUMER PRICE INDICES OR
TABLE 1
1970 THROUGH T9eGec
oie7
Natural Gas
108.
ioe
22
lez ae
143.
7 ee
20u
Zoo
265).
BO Sz
363.
414.
497.
580.
584.
556.
B23.
Or ££ RP NY WO HO W FP WN OH OO YO W NY WO
100
EVeGtt vemsee,
106.
Tae
i TSe
124.
147.
167.
La
oo
Z0er
Zeno
Za36
291.
Bia Ol
330%
Soe
BOT.
S20
rPmMm on ww Ww FP RP FF WH ODO MH OO WO N WN
New
Autos
LOge
i238
a
LL
Lig
2a
13: Si
142%
L538
166.
179%
190.
LS7.
2025
2087
219.
234
“I N Ol Oy Ol ® WO © © 70 =! OF OF owe
All
Items
11Ge
120
1252
133%
147%
16.8
170
1818
1952
2172
246.
2726
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298.
3.
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3256
J ff RP FP FP FP DO FP FON NN N RP WW W
Indices cited for 1985 and 1986 are the indices as of
U.S.
Department of Commerce,
of the United States,
the end of December 1985 and December 1986.
Statistical Abstract
1976 and 1986.
U.S. Department of Labor, CPI Detailed Report,
December 1985 and 1986.
14
The literature provided cost data on initial procurement
costs, maintenance costs, operating costs, and supporting
equipment costs of the alternative fuel vehicles.
The literature search provided points of contact for
additional information. Telephone interviews were conducted
with several electric vehicle manufacturers and the American
Gas Association. As a result of these telephone interviews,
additional research material was forwarded to the thesis
writer. This additional information included cost and
performance data.
The cost data derived from the above research was used
to compute a life cycle cost for each alternative fuel
vehicle type. The fuel cost rates used in the life cycle
cost determination were those rates paid by the Naval
Postgraduate School in 1986.
The life cycle cost of the gasoline-powered vehicle was
derived using 1986 cost data from the Naval Postgraduate
Sehool transportation office. Initial procurement cost,
operating cost per mile, and maintenance cost per mile are
the computed averages for all gasoline-powered sedans, vans,
and light trucks in the Naval Postgraduate School vehicle
fleet.
If the study were to determine that an alternative fuel
vehicle should be used in the transportation vehicle fleet,
there would be a fixed cost of the price of the fueling
Station. In the case of an electric-powered vehicle, the
isd
fueling station would be a charging unit. For a compressed
natural gas-powered vehicle, the refueling station would be
a natural gas compressor. Due to this fixed charge
component in the life cycle cost, a fixed charge linear
program was deemed appropriate for determining the optimal
mix of vehicle types in the vehicle fleet. Constraints in
the linear program were derived from the transportation
office budget and the operational requirements placed upon
the vehicle fleet.
H. SUMMARY
This thesis reviews the current state of the art in
electric-powered vehicles and compressed natural gas-powered
vehicles. A means of determining the mix of high and low
performance vehicles required to meet mission requirements
is submitted. A model for computing the life cycle cost of
a vehicle type is explained and then used in a fixed charge
linear program to determine the optimal mix of vehicles to
meet the requirements placed upon the vehicle fleet.
The models and linear program are tested by using the
Naval Postgraduate School transportation office vehicle
fleet as a test case.
Chapter II of the thesis evaluates the advantages and
disadvantages of each of the vehicle types. Based on the
range and maximum cruising speeds of the vehicle types, the
vehicles are classified as either high or low performance
vehicles.
16
In Chapter III, the cost components of the life cycle
cost model are explained and the life cycle cost model is
formulated. The costs associated with each vehicle type are
then put into the life cycle cost model to obtain the life
cycle costs for each vehicle type.
In Chapter IV, the fixed charge linear program model is
explained. The life cycle costs computed in Chapter III are
then put into the fixed charge linear program. The
constraints used in the fixed charge linear program are
based on the Naval Postgraduate School transportation
office's mission requirements and budget. By using the
fixed charge linear program, an optimal mix of vehicles for
the Naval Postgraduate School vehicle fleet is determined.
Le
Ii. ALTERNATIVES
This chapter begins with a brief description of the
electric-powered vehicle and how it operates. Performance
Gata derived from tests of various models of electric-
powered vehicles will be presented for use in classifying
the electric-powered vehicle as either high or low
performance. Cost data concerning the electric vehicle's
procurement cost, maintenance cost, and fuel cost will also
be presented.
Following the section on electric-powered vehicles, the
compressed natural gas-powered vehicle will be described.
Performance data will be presented as will cost data on
procurement, maintenance, and fuel.
As ELECTRIC—-POWERED VEHEGCEES
1. Background
At the beginning of the twentieth century, the
electric vehicle was in direct competition with the gasoline
powered vehicle. The scarcity of gasoline stations made the
electric vehicle a viable option to the gasoline vehicle.
However, with the rapid growth of the gasoline service
station industry came the demise of the electric-powered
vehicle. The demise of the electric-powered vehicle was
attributable to its limited range and unreliable power
source, the batteries. (Ref. l:p. 24]
iS
During World War II, due to gas_ shortages and
rationing of gasoline, there were approximately 6,000
electric-powered vehicles in operation in the United States.
Following the war, the growth of the electric vehicle
industry continued until it reached its highpoint in the
1960s when there were approximately 45,000 electric vehicles
in use in the United States. At that time, the electric
vehicle was mainly being used for delivery service in
industries such as the dairy industry. [Ref. l:p. 24]
An electric-powered vehicle with a range of 40 to 50
miles between chargings could be built with the technology
available today. An electric vehicle with this range would
be capable of meeting 95% of the daily driving needs of a
typical United States car owner. [(Ref. 2:p. 1388]
The electric vehicle manufacturing industry in the
United States consists mainly of small manufacturing firms.
Most of the United States electric vehicle manufacturers
believe that the most popular and efficient electric-powered
vehicle model is either the small passenger car or the small
van. The body design of the vehicle is most often a
conversion of an existing gasoline vehicle's body. (Ref.
mepp- 629-630 ]
Since the recent oil glut began in the early 1980s,
many of the small electric-powered vehicle manufacturers
have gone out of the electric vehicle production business
citing low demand for electric vehicles. However, the
19
electric vehicle industry continues to grow overseas,
especially in Great Britain.
The largest single test program of electric-powered
vehicles was conducted by the United States Postal Service.
The test began in August 1971. A total of 383 electric-
powered vehicles were used. The majority of the vehicles
were converted AM General Jeeps. The results of the test
will be included in the electric vehicle performance data
section of this thesis. [Ref. 3:p. 630]
2. Vehicle Description
The basic electric vehicle drivetrain consists of a
battery, a controller, a motor, a transmission, and a
differential layed out in accordance with the following
schematic.
Battery---Controller---Motor---Transmission---Differentital
The battery is the source of all the propulsion energy. The
controller regulates the power supplied to the motor. The
motor converts the power into rotary motion which the
transmission matches to that of the axle. Finally, the
differential balances the power supplied to each of the
drive wheels. [Ref. 4:p. 20]
a. The Battery
The Noyes Data Corporation in their 1979 book,
Electric and Hybrid Vehicles, states:
Batteries represent only 10 percent of the initial
cost of today's electric vehicle, yet the ultimate
20
operating costs of electric vehicles are heavily dependent
on battery performance. The energy and power available
from a battery directly affect the road performance of an
electric vehicle. The cycle life and maintenance
requirements contribute directly to the ultimate operating
cost, and the complexity of the battery system is directly
melated to reliabilaty. [Ref. 3:p. 347]
The most widely used type of battery is the
lead-acid battery similar to that used in gasoline-powered
vehicles. While there are other types of batteries such as
nickel-zince and nickel-iron, the lead-acid battery is the
most popular and will be the battery on which test results
and cost data are based.
There are four types of lead-acid batteries.
The starting, lighting, and ignition lead-acid battery is
the battery used in gasoline-powered vehicles. Another type
of lead-acid battery is the type used in most electric-
powered golf cars. The final two types of lead-acid
batteries are the semi-industrial and industrial. [Ref.
3:p. 350]
The starting, lighting, and ignition battery is
designed to deliver high power for short periods of time.
The golf car battery is designed to deliver high power for
relatively long periods of time while minimizing the battery
weight. The semi-industrial and industrial batteries are
not so much concerned with the weight of the battery as they
are the length of time the battery can deliver a high amount
of power. Based on its size and low weight, the golf car
Za
battery is the type of lead-acid battery most used in
electric-powered sedans and small vans. [Ref. 3:p. 350]
The deep-discharge life cycle of a battery
determines the useful life of a battery. For a golimieans
battery, the deep-discharge life cycle is estimated at 200
tom400m@eyVeles. For purposes of determining the life cycle
cost of the electric-powered vehicle, the deep-discharge
life of the golf car battery will be fixed at 300 cycles.
(Ref. Siipkes 52)
The performance of the battery is greatly
affected by its operating environment. The battery capacity
of a battery at 32 degrees F is only 60% of that of a
battery at 72 degrees F. Thus, the cold weather performance
level of an electric-powered vehicle will be much lower than
its warm weather performance level. Range of the vehicle
and its acceleration will be reduced due to the lower
battery capacity. [Ref. 3:p. 358]
The recharging of a lead-acid battery usually
takes between four and twelve hours. Overcharging was
batteries can lead to loss of water in the battery,
requiring additional maintenance and its accompanying costs.
Undercharging of the battery results in reduced range. The
controlling of the charging of the battery is usually done
by the battery charger. Present day chargers are not
capable of adjusting the charging period of a battery based
Z2
on temperature or the age of the battery. [RereweSe Dp. 363—
364]
beeethe Controller
The controller acts as the link between the
battery and the motor. It allows the electric vehicle
operator to control the amount of power which flows from the
battery to the motor. The controller should provide the
following:
(1) Smooth operation at and near zero speed for good
maneuverability and parking
(2) Smooth acceleration at the operator selected rate to
the desired speed
(3) Operation at any operator-selected constant speed
(4) Smooth deceleration where regenerative braking is
employed
(5) Efficient, safe, and reliable operation
(6) Overload protection for motors, motor reversing, and
charging of auxiliary batteries. [Ref. 3:p. 171]
Since all current electric vehicles use direct
current (DC) motors, the controller varies the voltage and
the current to the motor in order to control the flow of
power. feet. 3:0. 171]
The regenerative braking mentioned in (4) above
is a means of charging the battery through the use of the
energy loss which occurs when the vehicle brakes. In most
conventional vehicles friction brakes are used. The kinetic
energy loss resulting from braking a conventional vehicle is
lost in the form of heat. In the electric vehicle, the
kinetic energy loss can be recovered electrically and used
to charge the battery, thus extending the range of the
vehicle. In regenerative braking, the electric vehicle's
23
motor acts as a generator sending a charge to the battery
and a resistive load to the wheels thus braking the vehicle.
The controller must be able to control the amount of charge
flowing to the battery if regenerative braking is used in
the electric vehicle. [Ref. 5:p. 149]
c. The Motor
The direct current (DC) motor is the most
popular type of motor used in an electric vehicle mainly due
to the types of demands placed on an electric vehicle. The
DC series motor delivers a high torque per ampere ratio
under heavy loads thus reducing the battery drain of the
electric vehicle during acceleration or climbing hills.
(Ret. 33). 269)
dad. The Transmission
If the only means of varying the motor speed and
torque of the electric vehicle were the controller, the
electric vehicle would be unable to operate efficiently.
The transmission allows the electric vehicle to maximize the
power and the efficiency of the electric motor. It provides
better vehicle acceleration and hill climbing ability.
[Rei. . 3: pawl6 1)
The most common type of transmission used in
electric-powered vehicles is the manual shift multi-gear
transmission. The popularity of the manual transmission is
mainly due to its size, durability, efficiency, and low
price. sqRet 7303p. 16>)
24
Another popular transmission is the automatic
shift transmission whose shift points are designed to
Seincide with the motor'’s “characteristics. The main
disadvantages of this type of transmission are its higher
cost and weight, and its lower efficiency when compared to
the manual multi-gear transmission. [Ref. 3:p. 165]
The Continuously Variable Transmission (CVT) is
a transmission option which is currently being developed by
electric vehicle manufacturers. Its yet to be realized
goals are to offer the advantages of a fully automatic
transmission with the energy efficiency of a manual multi-
gear transmission. [Ref. 5:pp. 176-178]
e. The Differential
The differential is used to equally distribute
the load to the drive wheels when they rotate at different
Speeds aS in cornering. The differentials used in all the
current electric-powered vehicles are the conventional
differential found in gasoline-powered vehicles. [Ref. 3:p.
159]
3. Advantages of Electric-Powered Vehicles
The following are the claimed advantages of using an
electric-powered vehicle.
1. Increased Reliability. The long life and simplicity
of electric vehicle components will lead to more
reliability and lower probability of breaking down.
While most tests have actually found that electric
vehicles are no more reliable than gasoline-powered
vehicles, some electric vehicle proponents believe
that if production of electric vehicles were
25
increased, the reliability benefit would be realized.
PRef. 4¢pee212)
2. Low Maintenance. Scheduled and unscheduled
maintenance will be reduced by as much as two-thirds
of that required to be performed on gasoline-powered
vehicles. [Ref. 4:p. 212]
3. Less Dependence on Oil Imports. Since an electric
vehicle does not use gasoline, an increase in the use
of electric-powered vehicles would lower our
requirement for oil.
4. Less Pollution. Since electric vehicles do nowwoeuwen
gasoline there will be less pollution.
5. Less Noise. Electric-powered vehicles are quieter
than gasoline-powered vehicles. [Ref. 5:p. 8]
4. Disadvantages of Electric-Powered Vehicles
The following are the disadvantages associated with
using an electric-powered vehicle.
1. Lower Performance. The range of an electric-powered
vehicle is much lower than that of the gasoline-
powered vehicle. The maximum cruising speed and
acceleration rate of electric vehicles are also lower
than those of the typical gasoline-powered vehicle.
[Reis -42p.. 213]
2. More Expensive. The initial procurement cost and the
total life cycle cost of an electric vehicle is higher
than that of a comparable size gasoline-powered
vehicle based on current fuel and maintenance costs.
[Ref. 4:p. 214]
5. Electric-Powered Vehicle Performance Data
The performance measures which will be addressed in
this thesis are, first, range between chargings’9 and,
secondly, maximum cruising speed. These two performance
measures will be used to classify the electric-powered
vehicle as either a high or low performance vehicle.
26
The range of the electric-powered vehicle is a
function of the speed the vehicle is traveling and the load
placed upon it. The environment that the vehicle operates
in, the skill of the operator, and the vehicle's condition
also greatly affect the range of the vehicle.
The following test results are derived from data
reported by Noyes Data Corporation in its book Electric and
Hybrid Vehicles. Tests were conducted on 23 electric-
powered vehicles ranging in size from a two-passenger
vehicle to a van.
1. Maximum Speed: Values ranged from 31 miles per hour
to 56 miles per hour. The average maximum speed was
43 miles per hour. This is well below the high
performance parameter of 55 miles per hour maximum
cruising speed. [Ref. 3:p. 47]
2. Range at 25 miles per hour (constant speed): Values
ranged from 26 miles to 117 miles. The average range
at a constant speed of 25 miles per hour was 54 miles.
[Rete s > Dp. .47 |
3. Range at 35 miles per hour (constant speed): Only 11
out of the 23 electric-powered vehicles were able to
complete this test. The values ranged from 23 miles
to 88 miles. The average range at a constant speed of
35 miles per hour was 47 miles. [Ref. 3:p. 47]
4. Range at 45 miles per hour (constant speed): Only
five out of the 23 electric vehicles were able to
complete this test. The values ranged from 25 miles
to 71 miles. The average range at a constant speed of
45 miles per hour was 38 miles. [Ref. 3:p. 47]
Several tests were conducted to find the range of
electric-powered vehicles under stop and go - driving
conditions. These tests were conducted in accordance with
schedules written by the Society of Automotive Engineers in
SAE J227a, Electric Vehicle Test Procedure, dated February
Pat
1976. Each test was terminated when the test vehicle's
acceleration was insufficient to reach the required cruising
speed within the required time, although the vehicle could
continue to operate. [Ref. 3:pp. 39-41]
1. The first test simulated a fixed route in an urban
setting. The distances traveled until the next test
was terminated, ranged from 20 miles to 80 miles. The
average distance was 38 miles. [Ref. 3:pp. 41,47]
2. The second test simulated a variable route in an urban
setting. Twelve of the 23 vehicles were able to
complete this test. The distances traveled ranged
from 20 miles to 77 miles. The average distance was
36 miles. [Ref. 3:pp. 41,47]
The second stop and go driving test will be used to
judge overall vehicle range as it best approximates a
typical driving environment ona Navy base or station.
Based on the test results, the electric vehicle must
be classified as a low performance vehicle for both maximum
cruising speed and range reasons. The maximum cruising
speed is, on average, 43 miles per hour with 45 miles per
hour attainable on 5 out of 23 models tested. The range is
limited to about 36 miles between charges.
6. Electric-Powered Vehicle Cost Data
The cost data this thesis will review pertains to
initial procurement cost, fuel cost per mile of operation,
maintenance cost per mile of operation, battery replacement
cost, and battery charger cost.
A 1977 survey of manufacturers of electric vehicles
in the United States found that the initial procurement cost
of an electric vehicle ranged from $3300 to $10,800. The
28
cost of the electric vehicle was found to be roughly
proportional to its weight ($4 to $6 per kilogram). In
comparison, a gasoline-powered vehicle costs roughly $3 per
kilogram. This means that an electric vehicle's initial
procurement cost is anywhere from 34% to 100% higher than
that of a gasoline-powered vehicle. [Ref. 3:p. 93]
In doing life cycle cost estimates of electric-
powered vehicles for this thesis, it will be assumed that
the initial procurement cost is 1.5 times the average cost
of a gasoline-powered vehicle. The salvage value of the
electric vehicle is estimated at six percent of its
procurement cost. The salvage value is based on the scrap
metal value of the vehicle. [Ref. 6]
Fuel estimates for electric vehicles used by the
United States Postal were between 1.2 and 1.5 kilowatt hours
per mile of operation [Ref. 7:p. 739]. An electric-powered
vehicle requires approximately 40 kWh per battery recharge
(Ref. 5:p. 249]. Based on this refueling measure, the fuel
cost estimate per mile of operation can be derived by:
1. Dividing 40 kWh by the range of the electric-powered
vehicle. Based on the earlier test range of 36 miles,
the fuel estimate per mile of operation is:
40 kWh
Gear 1.11 kWh per mile
2. Then multiply the fuel estimate per mile times the
cost of a kWh of electricity.
The primary maintenance cost of electric-powered
vehicles is battery maintenance. The time required to
29
conduct battery maintenance is dependent on the number of
batteries, how hard it is to get them to conduct
maintenance, and the size of the batteries. Maintenance
costs also depend on how the batteries are being charged.
Overcharging leads to loss of battery fluid which requires
more than normal maintenance.
William Hamilton, in his article, "Costs of Electric
Vehicles inn peocal Fleet Service," states that the
Maintenance costs of electric-powered vehicles will be 65%
of the current cost to maintain gasoline-powered vehicles.
He derives this figure by determining what percent of a
gasoline vehicle's maintenance cost is directly attributable
to the internal combustion engine components of the vehicle.
[REE s. 3 pp< 3759-740 |
Further research has found no better means of
estimating maintenance costs, therefore Mr. Hamilton's
estimating tool of 65% will be used to figure the
maintenance cost per mile of operation.
The battery replacement cost for golf car type
batteries in 1979 was $50 per kWh [Ref. 3:p. 356]. Assuming
that the electric vehicle is using a 40 kWh battery, the
cost of replacing the battery would be $2000 in 1979
dollars. The life of the battery in terms of miles can be
figured in the following manner. It was assumed earlier
that a battery's deep cycle life was 300 cycles. The range
of the vehicle per cycle is 36 miles. Therefore, the life
30
of the batteries in terms of miles is 10,800 miles, 36 miles
per cycle x 300 cycle battery life. An experimental battery
constructed with nickel-zinc has attained a cycle life of
100 cycles. If the battery can be mass produced, the cost
per kWh is estimated to be $50 in 1979 dollars. {[{Ref. 5:p.
216]
According to Department of Energy studies, the range
in the cost of battery chargers for electric-powered
vehicles was $550 to $1300 in 1986. The more expensive
battery chargers offered options such as timers. The
average cost of a battery charger was estimated to be $650.
The expected life of the battery charger was 10 years with
no annual maintenance expenses forecasted. No special power
requirements or installation requirements accompanied the
purchase of the battery charger. [Ref. 8]
B. COMPRESSED NATURAL GAS-POWERED VEHICLES
ito bAackKoOround
The first practical natural gas power engine was
invented by Nicholas Otto in 1976, nine years before Karl
Benz built the first internal combustion engine-powered
vehicle. Since those early days, compressed natural gas-
powered vehicles have proven themselves to be ae safe
alternative to the gasoline-powered vehicle in = many
countries around the world. Hundreds of thousands of
compressed natural gas-powered vehicles are currently in
operation in countries such as Italy, China and New Zealand.
oak
In the United States and Canada there are approximately
30,000 compressed natural gas-powered vehicles on the road.
(Ref. 9:p. 46]
One hundred thirty-five utility companies currently
have compressed natural gas-powered vehicle fleets, up from
only 65 utility companies in 1984. [Ref. 10:p. 49]
In 1978, the United States Congress passed the
Natural Gas Policy Act which provided for gradual increases
in natural gas wellhead price ceilings. The legislation was
intended to tie the price of natural gas to the projected
"heat equivalent" price of oil in 1985. By 1985, the
majority of the natural gas industry was to be decontrolled.
With the rapid rise of oil prices which occurred in the late
1970s and early 1980s, the projected prices for natural gas
in 1985 were quickly exceeded (Ref. ll:p. ix]. In 1986, the
price of oil dropped and with it the price of natural gas
also decreased. By early 1987, the price of oil had begun
to rise drawing the price of natural gas higher also. The
parallel change in price of both oil and natural gas its
attributable to the fact that they are substitutes for each
other. A rise in the price of oil will cause demand for the
natural gas to increase thereby causing an increase in the
price of natural gas.
Since 1978, the percentage increase in the price of
natural gas has exceeded the percentage increase in the
price of gasoline. In 1978, the Consumer Price Index for
a2
natural gas was 263.1 and the CPI for gasoline was 196.3.
By 1984, the CPI of natural gas had risen to 584.4, while
the CPI of gasoline had risen to 370.2. [Ref. 12]
2. Vehicle Description
The compressed natural gas vehicle which has proved
to be the most popular with the general public is actually a
conversion of a standard gasoline-powered vehicle to a dual
fuel capable vehicle. Most gasoline-powered vehicles can be
converted to the compressed natural gas system in one day or
less. The conversion process does not require any major
engine modifications. All the conversion parts simply bolt
on. With the conversion kit installed the vehicle operator
can drive the vehicle using compressed natural gas fuel or
gasoline. The switchover procedure from one fuel to the
other is a simple flip of a switch. [Ref. 13]
The compressed natural gas conversion kit includes
the following parts: compressed natural gas cylinders, fuel
selector switch, regulator, fuel gauge transducer, filling
connection, gasoline solenoid valve, dual curve ignition
box, mixer, fuel gauge, master shut off valve, and gas
Teo nc . The following diagram, Figure 1, shows the major
parts, their functions, and their installed locations in a
typical sedan. [Ref. 14:p. 3]
The natural gas cylinders hold natural gas at a
pressure of 2400 pounds per square inch. Due to the high
pressure of the gas, no fuel pump is required to deliver the
a
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Vilar 1s
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wee Stee
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34
fuel to the mixer. The regulator controls the flow of
natural gas from the cylinder(s) to the mixer. The mixer
bolts onto the carburetor and insures the proper mix of
natural gas and air is fed into the carburetor and the
engine. The dual curve ignition box adjusts the ignition
timing to correspond to the fuel, gasoline or natural gas,
being fed into the carburetor. The fuel selector switch
allows the vehicle operator to switch the fuel source of the
vehicle without stopping the vehicle. The fuel selector
switch is located on the interior dash of the car as is an
added natural gas fuel gauge which keeps the driver informed
as to the amount of natural gas left in the cylinder(s).
meet. 1l4:p. 3)
3. Advantages of Compressed Natural Gas Vehicles
The following are the claimed advantages of a
compressed natural gas-powered vehicle.
a. Natural gas iS cheaper per gallon equivalent than
gasoline. The American Gas Association estimates that
it is 30 to 60% cheaper to refuel a car with
compressed natural gas than with gasoline. The
present cost of a gallon equivalent of natural gas is
between 45 cents and 85 cents. [Ref. 14:p. 1]
b. Natural gas burns cleaner than gasoline thus producing
less pollution. Natural gas burns lead-free and
produces almost no carbon monoxide. [Ref. 14:p. 1]
c. Natural gas reduces the maintenance required on
vehicles. Standard maintenance on vehicles that burn
natural gas is half that of gasoline-powered vehicles.
PRof .e44spre 1 |
dad. Natural gas is plentiful. Consumers don't have to
worry about any shortage of natural gas in the
foreseeable future. (Ret i= 14 py .< |
35
e. Natural gas is safer than gasoline. Compressed
natural gas cylinders are built to withstand abuse,
unlike the conventional vehicle gasoline tank. In the
event of a gas leak, natural gas, being lighter than
air, will dissipate rather than pool like gasoline.
The combustion point of natural gas is 1300 degrees F
while the combustion point of gasoline is much lower,
800 degrees F. [Ref. 9:p. 46]
4. Disadvantages of Compressed Natural Gas Vehicles
The following are the disadvantages associated with
converting a vehicle to compressed natural gas.
a. Few natural gas refueling stations. There are only
250 private refueling stations and five public
refueling stations located in the United States.
(Ref. 9p.) 49)
b. Limited range with natural gas as fuel. A typical
compressed natural gas cylinder holds enough fuel to
allow a range of between 40 to 90 miles. However,
with the dual fuel capability extended trips can be
made with a compressed natural gas converted vehicle.
[Ref. 9:p. 48]
c. Lower performance. The compressed natural gas-powered
vehicle loses approximately 10% of its horsepower when
it operates on natural gas rather than gasoline.
[Reft. “92p.7-238)]
ad. High fixed cost to convert vehicle fleet. In order to
have the ability to refuel a fleet of vehicles, a
company would have to purchase a cascade compressor
and its attendent filling station. This capital
outlay is the most expensive aspect of converting a
vehicle fleet to compressed natural gas. [Ref. Osioz
48}
e. Due to the installation of compressed natural gas
cylinders in the trunk or storage compartment of the
vehicle, the cargo capacity of the vehicle is reduced.
5. Compressed Natural Gas Vehicle Performance Data
The range of a compressed natural gas-powered
vehicle while operating on natural gas is a function of the
number of gas cylinders installed in the vehicle. Each gas
36
cylinder allows a range of between 40 and 90 miles,
depending on the size of the cylinder. However, the dual
fuel capability of the compressed natural gas-powered
vehicle allows it to be used for any trip that a
conventional gasoline-powered vehicle can make. Hoye 1) alsie!
reason, the compressed natural gas vehicle is considered a
high performance vehicle in the range performance area.
The use of compressed natural gas as a fuel results
in a 10% decrease in the power of the converted internal
combustion engine vehicle. While this loss of power affects
acceleration, it can be assumed that all converted vehicles
are capable of attaining the 55 miles per hour maximum
cruising speed needed to qualify as a high performance
vehicle in the cruising speed performance area.
Based on the range and maximum cruising speed of the
compressed natural gas-powered vehicle, it is classified as
a high performance vehicle.
6. Compressed Natural Gas Vehicle Cost Data
The initial procurement cost of a compressed natural
gas-powered vehicle is the sum of the average cost of a
gasoline-powered vehicle and the average cost of the
conversion kit. In 1984, the average cost to convert a
sedan to natural gas for 120 U.S. gas utility company
vehicle fleets was approximately $1,521, while the average
cost to convert a van or small truck to natural gas was
ps9 4 (Ref. 15:p. 22]. The average of these _ two
37)
installation costs is $1,555. The 1986 adjusted cost of
installation, using the adjustment factors in Table 1, is
$1,628 ((1555/3012 2) eee ore Therefore, the initial
procurement cost of the vehicle used in this thesis is:
Average cost of gasoline vehicle + $1,628
While the installation of the conversion kit adds some value
to the vehicle, the salvage value will be estimated at 10%
of the initial procurement cost of the gasoline-powered
vehicle before conversion took place.
Since this thesis 1S concerned with fleet vehicles,
a decision to convert to compressed natural gas-vehicles
would require the purchase of a cascade compressor and
filling “station. A 30 cubic foot per minute (CFM) cascade
compressor refueling system, capable of refueling 30
vehicles at a time, would cost $75,000 [Ref. 16:p. 8]. In
1982, a cascade compressor and filling station capable of
refueling nine vehicles per hour would cost approximately
$44,000 installed [ReEf. 6 :ppreysé Saiz A small compressor
capable of handling one or two vehicles per hour would cost
around $7,000 installed {Ref. 1423p 2978 The small
compressor would take too long to refuel vehicles while the
30 CFM compressor would probably exceed the refueling
requirements of most Navy commands. Therefore, the
investment cost for the compressor and filling station used
38
in this thesis will be the $44,000 option adjusted to 1986
gdomlars (1.e., $49,570).
As of 28 February 1986, the national average price
for a gallon equivalent of natural gas was 93 cents. The
cost of natural gas to vehicle fleet users was $0.72 ona
national average basis. The average small truck or van will
get around 15 miles per gallon. Therefore, the average cost
of fuel per mile of operation for a compressed natural gas-
powered vehicle is approximately five cents for fleet users.
[Ref. 16:p. 2]
The American Gas Association claims that the
maintenance costs of compressed natural gas-powered vehicles
is half that of gasoline-powered vehicles [Ref. 14:p. 1].
This claim is based on the fact that natural gas is a clean
buemning fuel so oil, spark plugs, and points will not
require changing as often as in a gasoline-powered vehicle.
In Mr. Hamilton's review of internal combustion engine
maintenance costs, he found that the ignition system
maintenance costs and the lubrication costs amounted to
roughly 14% of the total maintenance cost of an internal
combustion engine vehicle [Ref. 7:p. 740]. Therefore, an
extension of the life of the oil, spark plugs, and points to
double their normal life would only result in a savings of
7% of the maintenance cost. For the purposes of this
thesis, the maintenance cost of natural gas vehicles will be
39
estimated at 75 percent of the maintenance cost of gasoline-
powered vehicles.
The conversion kit's useful life is at least equal
to the life of the vehicle in which it is installed [Ref.
6:p. 57]. The American Gas Association estimates the useful
life of the compressor to be 10 years with annual operations
and maintenance expenses for the compressor being equal to
12 cents per gallon equivalent of natural gas pumped [Ref.
ey a
40
(Meee tobe CrCbE COS) MODEL
Department of Defense Instruction 7041.3, dated 18
October 1972, defines economic analysis as:
A systematic approach to the problem of choosing how to
employ scarce resources and an investigation of the full
implications of achieving a given objective in the most
efficient and effective manner.
The instruction goes on to require an economic analysis be
performed for proposals whenever there is a "choice or
trade-off between two or more options even when one of the
options is to maintain the status quo or to do nothing."
Beets 128: pp. 2-3]
A major portion of the economic analysis is the cost
analysis. DOD Instruction 7041.3 requires that life cycle
cost estimates be prepared for all program alternatives when
feasible. The instruction defines life cycle costs to
include "all anticipated expenditures directly or indirectly
associated with an alternative." The InSserUuection
specifically states that "sunk costs," costs which have
already been incurred prior to conducting the analysis, are
excluded from the cost analysis. [Ref. 18:p. 2]
The life cycle cost estimate begins with an estimate of
outlays for each year of the "economic life" of the
alternative. The economic life of an alternative is the
period of time that an alternative is capable of providing
the service it was designed for. [Ref. 18:p. 7]
4Al
Once the yearly outlay estimates have been made, a
discount factor is applied to each year's outlays to
determine the net present value of the alternative. The
discount factor is used to recognize that there are
differences in the timing of expenditures. A dollar spent
today 1S more valuable than a dollar that will be spent two
years from today. {Refs 18: ppe, S67]
In the civilian business environment, the discount
factor is based on the cost of acquiring additional capital.
In the Department of Defense, the discount factor is based
on a 10% interest rate. The discount factors for the
Department of Defense are listed in Table 2. [Ref. 18:p. 6]
TABLE 2
DEPARTMENT OF DEFENSE DISCOUNT FACTORS
Present Value of $l
Project Year 10% Discount Factor
ili 0.954
Z O=2S67,
3 0.788
4 Sls Wik y
5 0.652
6 02592
7 O53 36
8 0.489
9 0.445
10 0.405
Source: Department of Defense Instruction 7041.3,
dated 18 October 1972.
42
The alternative which is found to have the lowest
average cost per year is considered to be the most
SEelewent. [|Ref. @e2p2e7)
Pee GLFE CYCLE COST COMPONENTS
The major groups of costs which can be included in a
life cycle cost estimate are:
1. Research and development costs
2. Investment costs
3. Operations costs. [Ref. 18:pp. 2-5]
The Department of Defense has not invested funds in the
research and development of either electric-powered vehicles
Or compressed natural gas-powered vehicles, so research and
development funds will not be entered into the life cycle
eest Lormula.
Investment costs are costs associated with the purchase
of real property, equipment, non-recurring services or
operations, and maintenance start-up costs. Investment
costs do not necessarily occur in only Year 1 of a
procurement.
Investment costs can be either fixed or variable. Fixed
investment costs equate to fixed costs in the civilian
business environment as they are the fixed cost of choosing
a particular alternative. Being a fixed cost, the amount
does not vary with units of production, or in the case of
this thesis, vehicles in a particular fuel category. An
43
example of a fixed investment cost would be a refueling
station. {Refs “19% pnw]
Variable investment costs are tied to the volume GLE
option. An example of a variable investment cost is the
initial procurement cost of a vehicle. The variable
investment cost rises with each vehicle procured. (Ref.
LJs Dp.) /4 |
Operations costs, or recurring costs, are costs such as
personnel, material consumed during operations, overhead,
operating expenses and other annual expenses. The choice of
either of the alternative vehicles for use in the fleet
would not necessitate any additional personnel or overhead.
The recurring cost affected would be material consumed,
mainly fuel and maintenance costs. [Ref. 18:pp. 4-5]
Recurring costs such as fuel and maintenance costs are
classified as variable costs by civilian businesses in that
they vary directly with the units of output or, in the case
of this thesis, the number of vehicles in a particular fuel
category. Another common business term for variable costs
1s direct costs. ‘“[Ref. 192p. (7a
Be LIFE CYCLE COST FORMULA
The following life cycle cost formula was presented by
Dr. Dan Boger of the Naval Postgraduate School at the
Defense Logistics Agency Operations Research and Economic
Analysis Workshop in Virginia Beach, Virginia, on 6 December
Toe5. The ~title— “of pr. Boger's presentation was
44
"Alternative Vehicle Propulsion and the Optimal Industrial
Fleet." [Ref. 20]
Lecis = fiz + CijXij
where:
1 = vehicle type
J = propulsion type
LCCi4 = life cycle cost for alternative i,j
fj = fixed investment for alternative i,j
Cij = unit variable LCC for alternative i,j
Xj4j = number of units of alternative i,j.
The formula gives the user the option to deal with
various types of vehicles. Due to data limitations at the
Naval Postgraduate School Transportation Office, this thesis
will deal only with different types of propulsion, therefore
the i variable will not change.
The total life cycle cost formula is broken down into
two sub-formulas. The first sub-formula is used to compute
the unit variable life cycle cost for the alternative i,j.
st
Jk
Cij = Pijo + eerie * ey
where:
Pijo = unit procurement cost of alternative i,j
OCijt = unit operating cost of alternative i,j in year t
45
st = discount factor in year t
Sjj = unit salvage value for alternative i,j
KF
ll
the number of years in the economic life of the
vehicle.
The second sub-formula is used to calculate the unit
operating cost of alternative i,j in year t.
where:
Cit = ™itleje eee eee
Mj;+ = annual miles for vehicle type i in year t
est = cost/mile for fuel of type j in year t
Nijt = maintenance cost/mile for alternative i,j in
year t
Pijt = unit procurement costs for alternative i,j
in year t.
C. GASOLINE-POWERED VEHICLE LIFE CYCLE COST
The best way to explain the use of the life cycle cost
formula and its sub-formula is through an example. The
gasoline-powered vehicle will be classified as propulsion
type 1. The following data were gained through a review of
the 1986 records of the transportation office of the Naval
Postgraduate School [Rets. 21,22].
1
Zi
Number of vehicles subject to study: 62
Total initial procurement (investment) cost of subject
vehicles in 1986 dollars: $506,274
Total miles driven by subject vehicles in 1986:
313,000
Total fuel cost for subject vehicles in 1986:) 5177557
46
Total maintenance cost for subject vehicles in 1986:
2736s
Estimated average economical life fone subject
vehicles: 8 years
Estimated average salvage value for subject vehicles:
10% of initial procurement cost.
Using the above data, the life cycle cost for gasoline
vehicles at the Naval Postgraduate School is computed as
follows:
ie
Beginning with the sub-formula for unit operating cost
of alternative i,1 in year t, computations are as
follows:
as snnucshemmhes for vehicle type + in year t (m;+)
Benoa |
—75-— = 5048 miles
Pe occ iiehe FOtmerlclor type 1 am year — (e+)
do
c. Maintenance cost/mile for alternative i,1 in year
e (jit)
Za Oe
dad. There are no unit procurement costs in any year
other than year 0 so pjj+ = O.
Using the figures computed above the unit
operating cost of gasoline vehicles in year t is:
Oj1t = 5048(.0561 + .0874) + 0 = $724
The next step is to compute the unit variable life
cycle cost for the gasoline alternative (cj).
47
a. The initial unit procurement cost of gasoline
vehicles in years OM nig) aeeoe
506,274
=~5 ae = $87 oe
b. Next, the unit operating cost computed previously
is multiplied by the discount factors for years
one through eight, its economic life. The
products are then added together to get the total
discounted operating cost for the economic life of
the vehicle.
al
Y o4,tst = ((724 x .954) + (724 x .867) + (724 x .788)
t=1 ss. t(724 com
= $4,053
The total discounted fuel cost was $1,584, while
the discounted maintenance cost was $2,469.
c. The unit salvage value is the estimated salvage
value of the vehicle times the discount factor in
the year it is salvaged. The gasoline-powered
vehicle has an eight year economic life with a
Salvage value of 10% of its initial procurement
cost. The initial procurement cost was $8,166, so
its salvage value is $817 x .489, the discount
factor in year eight. Therefore,
§ls;, = $400
Putting the above computations into the formula, the
unit variable life cycle cost for the gasoline-powered
vehicle equals:
8,166 + 4,053 - 400 = $11,819
3. The final step in computing the life cycle cost for
the gasoline vehicle alternative is to figure out the
fixed investment costs for the alternative and the
number of vehicles using gasoline. The fixed
investment cost of choosing gasoline equals zero.
48
This is due to the prior purchase of all the equipment
and facilities required to maintain and operate the
gasoline vehicles. These prior expenditures are now
considered "sunk costs" and are excluded from the cost
analysis. The number of vehicles using gasoline in
the optimal solution is unknown. Thus the final life
cycle cost formula for the gasoline-powered vehicle
Option 1s:
O° + 11,819xj4
Bo BLECTRIC—-POWERED VEHICLE LIFE CYCLE COST
The life cycle cost for the electric-powered vehicle
will be derived by using the cost data that were determined
in Chapter II. The electric-powered vehicle will be
classified as propulsion type 2.
The computations for the unit operating cost of the
electric-powered vehicle in year t are as follows:
1. Annual miles for vehicle type 2 are the same as the
gasoline-powered vehicle, 5048 miles.
2. The fuel efficiency rating of the electric vehicle is
1.11 kilowatt hours per mile of operation. The cost
to the Naval Postgraduate School for a kilowatt hour
Siwclectrewerty se rougniy SO0708, according to the
Public Works Office. Therefore, the cost/mile for
fuel is:
1.11 x .08 = $0.0888
3. It was decided in Chapter II that the maintenance cost
of the electric vehicle would be estimated at 65% of
the maintenance cost of the gasoline-powered vehicle.
The gasoline-powered vehicle maintenance cost per mile
was determined to be $0.0874. Therefore, the
maintenance cost per mile of operation for the
electric-powered vehicle is:
sOomeeOG74 = 50.0568
49
4. Due to the 10 year economic life of the battery
charger it will not have to be replaced during the
life of the vehicle. The batteries have an estimated
life of 10,800 miles. Based on the average annual
miles of 5048, the batteries would require replacement
every 2.14 years or roughly every two years. The
replacement cost was estimated to be $2,000 in 1979,
this equates to $2996 in 1986, based on the "All
Items" consumer price index in Table 1. Battery
replacement expense of $2,996 should be expected in
years 3, 5, 7, and 9 of the analysis. If the
experimental nickel-zinc batteries are perfected, the
batteries would have to be replaced every seven years
at a replacement cost of $2,980.
Putting the above data into the unit operating cost formula,
the unit operating cost for an electric-powered vehicle in
years 1, 2, 4, 6, 8, and 10, is determined to be:
5048(.0888 + 20568) + )05— S7ea
In years 3, 5, 7, and 9, the unit operating cost for an
electric-powered vehicle is found to be:
5048(.0888 + .0568) + 2,996 = $3,731
The unit variable life cycle cost for the electric
vehicle is computed as follows:
1. The initial procurement cost of the electric vehicle
was estimated to be 1.5 times the initial procurement
cost of the gasoline-powered vehicle. The initial
procurement cost of the gasoline-powered vehicle was
determine to be $8,166. Therefore, the initial
procurement cost of the electric-powered vehicle is:
1.5 x 8,166 = $12,249
This initial procurement cost includes a battery
charger.
50
The wnt emm@peratingescost™ for the electric vehicle
($735) is multiplied by the discount factors for each
appltedable== year), 2, 4,6, 8, 10) and the unit
operating cost including battery replacement ($3731)
for years 3, 5, 7, and 9, is multiplied by the
appropriate discount factors. For years 1, 2, 4, 6,
8, and 10, the computations would be:
((735 x .954) + (735 x .867) + (735 x .717) +
(735 x .592) + (735 xX .489) + (735 x .405))
The sum of these products is $2,956. For years 3, 5,
7, and 9, the computations are:
(esl sore 7SS yee (s7emes 1.652) + (3731 x .538)
+ (3731 x .445))
The sum of these products is $9,039. The sum total
for all the years of the electric vehicle's economic
life is $11,995. Of this total, fuel cost amounts to
$2,886, and maintenance, which includes replacing the
batteries, amounts to $9,109.
The salvage value of the electric-powered vehicle was
estimated to be six percent of the initial procurement
cost of the vehicle. Therefore, the unit salvage
value equals ((12,249 x .06) x .405) = $298.
inserting the above computations into the unit
variable life cycle cost formula, the ten year unit life
cycle cost for the electric vehicle is determined to be:
12,249 + 11,995 - 298 = $23,946
To find the eight year life cycle cost, the ten year unit
life cycle cost is divided by 10, then the quotient is
multiplied by eight. The resulting eight year unit life
cycle cost is $19,157. The eight year unit life cycle cost
for fuel would be $2,309, with the eight year unit life
cycle cost for maintenance totalling $7,287.
Sl
The next step is to compute the life cycle cost for the
electric-powered vehicle alternative. Here the cost of
making the decision to use electric-powered vehicles is
recognized. The cost of making the decision is equal to the
cost of procuring the vehicles plus the cost of procuring
Support equipment or facilities.
The cost to procure a battery charger is included in the
vehicle procurement ' cost. No special facilities are
required as the battery charger can run off standard
electric current of 110 volts. Therefore, the life cycle
cost formula for the electric-powered vehicle alternative
ne.
O + 19,157x45
E. COMPRESSED NATURAL GAS-POWERED VEHICLE LIFE CYCLE COST
The compressed natural gas-powered vehicle will be
classified as propulsion type 3. Its life cycle costs will
computed using the cost figure derived in Chapter II.
The unit operating cost of alternative i,3 in year t is
computed as follows:
1. Annual miles for the vehicle type is 5048 miles.
2. The fuel cost per mile is $0.05.
3. The maintenance cost per mile was estimated to be 75%
of the gasoline vehicle, .0874 x .75 = .066.
4. The only unit procurement costs occur in year 0.
Therefore, the unit operating cost of a compressed
natural gas-powered vehicle in year t =
5048 (.05 + .066) + 0 = $586.
D2
The unit variable life cycle cost for the compressed
natural gas-powered vehicle is computed below:
1. The initial procurement cost of the compressed natural
gas vehicle was estimated to be the initial
procurement price of a gasoline-powered vehicle plus
$1,628. Therefore, the initial procurement cost of a
compressed natural gas vehicle is:
8,166 + 1,628 = $9,794.
2. The sum total of the compressed natural gas vehicle's
unit operating cost of $586 times the discount factors
in its eight year economic life is $3,280. The fuel
cost portion of this total is $1,410, while
maintenance costs amount to $1,870 during the eight
year economic life.
3. The salvage value of $817 times the discount factor in
year eight of .489 yields a unit salvage value of
$400, the same as that of the gasoline-powered
vehicle.
Putting the above computations into the life cycle
cost formula, the life cycle cost for the compressed natural
gas-powered vehicle is determined to be:
9,794 + 3,280 - 400 = $12,674
The life cycle cost for adopting the compressed natural
gas vehicle into the Naval Postgraduate School vehicle fleet
would be the fixed investment cost of building and equipping
a compressed natural gas refueling station plus the variable
life cycle cost of a compressed natural gas vehicle times
the number of compressed natural gas vehicles in the fleet.
The compressed natural gas refueling station was determined
bemeecOst $44,000 in 1982 or $49,570 in 1986 dollars.
3
Therefore, the life cycle cost of the compressed natural gas
vehicle alternative ws:
49,570 + 12,674xj43-
Life cycle cost computation worksheets are included as
the Appendix of the thesis.
54
IV. THE LINEAR PROGRAMMING MODEL
Linear programming is an advanced mathematical
programming technique which has found wide use in the
business environment. It deals only with problems where the
relationships between the variables are linear. For
example, when a vehicle is purchased a price is paid. cles
two of the vehicles are purchased, the purchaser would have
to pay twice as much. The relationship between price and
quantity in this example is a linear relationship. (Ref.
ep. 2)
Linear programming was developed in the late 1940s by
Professor G. Dantzig. It was widely used in the late 1950s
by petroleum companies to determine the best mix of gasoline
and heating oil the companies should produce in order to
maximize their profits. Various linear programming models
were developed to help the petroleum companies deal with
pipeline and tanker problems. [Ref. 23:p. 2]
Linear programming provides business managers a
mathematical tool to help them allocate scarce resources to
achieve an objective. Some examples of objectives would be
to maximize profit or minimize costs. Linear programming
will find the very best solution to a given problem and it
will indicate when there are equally good alternative
semtr1ons. (Ref. 23:p. 2]
22
The business manager uses linear programming by looking
at a real world problem and describing it in a mathematical
model which consists of a linear objective function and
linear resource constraints. [Ref. 24:p. 25}
The three principal steps in developing a linear
programming model are:
(1) the identification of solution variables (the
quantity of the activity in question),
(2) the development of an objective function that is a
linear relationship of the solution variables, and
(3) the determination of system constraints, which are
also linear relationships of the decision variables,
that reflect the limited resources of the problem.
(Ref. 24:p. 26]
Due to the fixed investment that would ensue if
compressed natural gas-powered vehicles were used in the
fleet, the fixed charge integer linear programming model
will be used in this thesis. In an integer linear program,
some or all of the solution variables are required to be
integers. [Refs 25:p. vi)
Integer programming was pioneered in the late 1950s by
Ralph Gomory. The advantage of an integer program is that
the solution will be in integer form. With a non-integer
linear program, non-integer solutions are often computed.
In this thesis, a non-integer solution would not be helpful
as one cannot use half a vehicle. [Ref. 25:p. vii]
In fixed charge problems, if the decision made is to go
with an alternative, there is a fixed charge inherent in
making that decision [Ref. 25:p. 18]. In this thesis, the
fixed charge would be the cost of building and equipping the
56
compressed natural gas refueling station. Even before one
vehicle has joined the vehicle fleet, there would be an
expenditure of funds which is not a linear cost of operating
the compressed natural gas vehicle.
In setting up a fixed charge model, a decision variable
is put in the objective function. The decision variable has
two values, 1 or O. If the value of the decision variable
is 1, the alternative is adopted and the fixed charge will
be expended. If the value of the decision variable is 0,
then the alternative is rejected and the fixed charge is
bypassed.
A. FIXED CHARGE INTEGER LINEAR PROGRAM MODEL
In his presentation at the Defense Logistics Agency
Workshop, Dr. Dan Boger explained the following integer
programming model which can be used for deriving the optimal
vehicle fleet. [Ref. 26]
The integer programming model is:
minimize ) ee fa Ve
Ls Mia 2 J ab yy
subject to the following constraints:
(1) 2 2 Pijoxij + fij¥ij < Po
1 oJ
t=8
(| c~7 II
(2) i) eijtxij < E
ic aa
ao)
t=8
ee) ete) Ss
C=
(4) ie er
(5) oi eee cia
(6) Peay =F
i oJ
where:
Ci; = unit variable life cycle cost for alternative i,j
xij = integer number of units of alternative i,j
fi4 = fixed investment costs for alternative i,j
Vij = decision variable for alternative i,j
Pijo = unit procurement costs in year O for alternative
1,)
Cijt = fuel costs in year t for alternative i,)
E = total fuel costs for eight year life cycle for
all fleet vehicles
mMijt = maintenance costs in year t for alternative i,j
M = total maintenance costs for eight year life cycle
for all fleet vehicles
Po = total investment costs in year 0
ujj = upper limit on number of units of alternative i,j
1ij = lower limit on number of units of alternative i1,j
F = number of vehicles in vehicle fleet
The fixed charge objective function for the above
integer programming model is:
Mamaml Ze a) Cy sc neeer nye
al
58
where:
ee Oman 1S saneinteger
Vem =O. Or 1
ele VY 3 uaa 0
The following budget and performance constraints were
placed on the optimal vehicle mix for the Naval Postgraduate
School vehicle fleet [Ref. 27]:
1. At least 30 of the 62 vehicles must be gasoline-
powered in order to meet current vehicle taskings.
2. Fleet life cycle fuel expenditures must not exceed
$189,000.
3. Fleet life cycle maintenance expenditures must not
exceed $183,000.
Inserting the values for the variables which were
computed in Chapter III and the budget and performance
constraints delineated above, the vehicle mix formulation
problem becomes:
Meemimize 11819x, + 19157x5 + 12674x3 + Oy, + Oyo + 49570y,
subject to
(1) 8166x, + 9799x5 + 9794x3 + Oy, + Oy + 49570y3 < 540,000
(2) 1584x, + 2309x> + 1410x; < 189,000
(3) 2469x, + 7287x5 + 1870x3 129, C00
(4) x7 = Olay <0
a9
(5) X95 -32y> <0
(6) X3 ="O2ZY3 < 0
Cy) aed) oe +30yYj < O
The first constraint is a budget constraint on the total
investment cost in year 0. The constraint covers both fixed
investment and variable investment costs. The right hand
Side value of the constraint is derived by computing a 95%
confidence interval for vehicle procurement costs for the
Naval Postgraduate School fleet of 62 vehicles.
The second constraint is a budget constraint on the
amount of funds that can be spent on fuel during the eight
year life of the fleet vehicles. The right hand side of the
constraint is computed using a 95% confidence interval based
on 1986 Naval Postgraduate School fuel expenditures.
The third constraint is also a budget constraint but it
limits the amount of funds which can be spent to maintain
the 62 vehicle fleet during its eight year life cycle. The
right hand side is computed using a 95% confidence interval
based on the 1986 maintenance costs for the Naval
Postgraduate School fleet of 62 vehicles.
The fourth through seventh constraints are on the number
of vehicles of each fuel type that may be included in the
optimal fleet mix. The fourth constraint limits the number
of gasoline-powered vehicles that may be included in the
optimal max to 62. The fifth constraint limits the number
60
of electric-powered vehicles that may be in the optimal mix
to 32. This coincides with the operational requirement that
at least 30 of the 62 vehicles be gasoline-powered. The
sixth constraint limits the number of compressed natural
gas-powered vehicles to 62. All vehicles in the optimal mix
may be compressed natural gas vehicles due to their dual
fuel capability. The seventh constraint insures that at
least 30 of the vehicles in the optimal mix are capable of
using gasoline as a fuel source.
When the above problem was run through the integer
program, the optimal mix of vehicles was computed to be 62
gasoline-powered vehicles. The net present cost of
purchasing, operating and maintaining these vehicles for an
eight year life was computed to be $732,778.
The above integer program would be useful to the Navy
Transportation Officer if he were to have control of the
funds required to procure the vehicles for his command.
However, the Naval Facilities Engineering Command,
Chesapeake Division (ChesDiv), located in Washington, D.C.,
is the central procurement activity for vehicles for the
Navy. Vehicles purchased by cChesDiv are sent to Navy
commands, who then make decisions as to what vehicles will
be retired from service. The individual command
transportation officers do not have an input into the
procurement process unless they require a vehicle in
addition to their present allowance.
61
The funds required to build a compressed natural gas
refueling station would be justified through a one time
budget augment request consisting of a request for Other
Procurement, Navy (OPN) funds and minor construction funds.
The budget augment request would be filed through the
command's chain of command during the annual budget cycle.
The justification for these funds would be a projected
Savings due to the use of alternative fuels rather than
gasoline in fleet vehicles.
In order to approach the optimal mix problem from the
viewpoint of the individual command transportation officer,
the following integer program is proposed:
Minimize 4053X, + 9596X5> + 3280x5 + Oy) + Oyen
Subject to
(1) 1584x, + 2309x5 + 1410x3 < 189,000
(2) 2469x, + 7287x5 + 1870x3 < 183,000
(3) X71 - 62y) < 0
(4) X95 ae yO <a
C5) X3 - 6230
(6) =a) — Xa 43 0v < 0
This integer program recognizes only the funds that the
individual command has control over. The objective function
62
consists of the life cycle fuel and maintenance costs
attributable to each of the vehicle propulsion types and
ignores salvage values because these funds are not returned
to the command disposing of the vehicle.
The constraints are the same as the first integer
program with the exception that the constraint dealing with
initial investment costs is deleted since the command has no
control over these funds.
The optimal mix derived from this integer program would
provide the lowest cost vehicle fleet in terms of annual
Operations and Maintenance, Navy funds.
When the above formulated problem is run through the
integer program, the optimal solution is found to be 62
compressed natural gas-powered vehicles. The O&M,N cost of
operating the 62 vehicle fleet of compressed natural gas
vehicles for the eight year life of the vehicles would be
£203,360.
A third situation to consider is the establishment of a
new transportation fleet at a base where no refueling
Capabilities presently exist. The cost of building a two-
pump gasoline refueling station is estimated to be $150,000
(Ref. 28]. Assuming that the experimental nickel-zZinc
batteries were installed in the electric vehicle, the
problem would be formulated as follows:
63
LiSdox a 4655 x50 1267 4x33 150000y 4 + OY5 + 49570Y3
subject to
8166x, + 9799x> + 9794x3 + 150000y, + Oyy + 49570y3 < 660000
1584x, + 2309x> + 1410x3 < 189000
2469X%4 °F 9 2763x%5 54 oo Ox, < 183000
“7 = OZ yaa < 0
X5 - 32y5 <0
x3 - 62y3 <0
~x4 - Xz + 30y) ne
When the above problem was run through the integer
program, the optimal vehicle mix was found to be 62
compressed natural gas vehicles. The net present cost of
procuring, operating and maintaining the fleet was computed
to be $835,358.
Bs SUMMARY AND CONCLUSIONS
This thesis has developed and explained a model for
determining the life cycle cost of alternative fuel
vehicles. Using the life cycle cost and requirement data
particular to a command, the integer linear program model
can be used to determine the optimal mix of vehicles for the
command's transportation fleet.
64
The thesis has looked at three ways the models can be
used. The first case was that of an established base with a
gasoline refueling station in operation. Due to the high
cost of procuring the compressed natural gas refueling
station and the high life cycle cost of the electric
vehicle, the optimal solution was found to be an entire
fleet of gasoline vehicles.
The second case looked at minimizing the = annual
operations and maintenance expenditures on the
transportation fleet while ignoring the initial investment
costs. The integer program found a fleet of compressed
natural gas vehicles would require the least expenditure of
operations and maintenance funds.
The third case looked at the problem of establishing a
new transportation fleet at a base which does not have any
refueling capabilities at the present time. The high cost
of the gasoline refueling station more than offsets the cost
of the compressor and conversion kits for the compressed
natural gas vehicles. Again, the optimal solution was found
to be an entire fleet of compressed natural gas vehicles.
The electric vehicle was found to have much too high a
life cycle cost to enter into the optimal mix, even though
it had no fixed investment cost. In the third case, the
experimental batteries were factored into the life cycle
cost but the reduction in life cycle cost was still too
small to make the electric vehicle an economic solution.
63
The compressed natural gas vehicle appears to be a
feasible alternative to the gasoline vehicle. The factors
which seem to impair its competition with the gasoline
vehicle are:
1. The scarcity of compressed natural gas refueling
stations. The number of refueling stations would not
be expected to increase until the number of vehicles
using compressed natural gas increases.
2. The price of natural gas, a relatively abundant
natural resource, is tied to the price of petroleun,
an increasingly scarce natural resource, by the
Natural Gas Policy Act of 1978. With this dependency
on the price of oil, the price of natural gas is
inflated to a level which does not justify the
additional investment in conversion kite and
compressed natural gas refueling stations for little
or no savings will accrue.
3. The high cost of the conversion kits. The conversion
kits are specialty items not offered by automobile
manufacturers, thus the cost is high and the
maintenance or conversion kit parts is very
specialized.
The above factors are interrelated with the price of
natural gas being the major obstacle in the compressed
natural gas vehicle's future. If the price of natural gas
can drop to a level significantly below that of gasoline,
its attractiveness as a vehicle fuel will increase. Savings
from lower fuel costs would justify investment expenditures
by large businesses, state and local governments. This
would increase the number of CNG-vehicles on the road,
leading to an increase in compressed natural gas refueling
stations. Increased popularity of compressed natural gas
would lead automobile manufacturers to offer factory
equipped CNG-vehicles. The mass production of the CNG-
66
vehicle would lower the additional cost for the CNG-
conversion kit as well as increase the number of maintenance
facilities capable of repairing CNG conversion systems.
67
APPENDIX
VEHICLE LIFE CYCLE COST COMEUTZA LIONS
Item 0
Fixed
Invest. 0
Vehicle
Invest. 8166
Fuel
Cost
Daseounte
Factor
Dirse-
Fuel
Cost
Maint.
Cost
Pase.
Maint.
Cost
Salvage Cost
GASOLINE-POWERED VEHICLE
LIFE CYCLE COST COMPUTA Peis
283
~954
276
Total
441
421
Year
2 3 +
235 Zoo Zio
so O/. se 2 OS . agely
245 225 203
Discounted Fuel
441 441 441
382 348 316
Zo5 283 283 “Zee
-652 .592 .538 3eiae
185 168 152 _
Cost = $1,584
441 441 441 441
288 261 23/ 2ake
Total Discounted Maintenance Cost = $2,469
Discounted Salvage Cost
Disc.
Yearly
Cashflows
Discounted Unit Life Cycle Cost = $11,
Discounted Alternative Life Cycle Cost
8166
690) 627 al
67
(817)
(400)
473 429 389 (46)
819
= 0 ye ldeae sr
Pit Ge lRane— POWERED VEHICLE
Mp eeerels COST COMPUTATIONS
Year
Item 0 alt 2 3 4 5 6 7 8 9 LO
Fixed
Invest. 0
Vehicle
Invest. 12249
Fuel Cost 448 448 448 448 448 448 448 448 448 448
Discount
Baccor Dopo G ee 7 Gomme To oOo e. 2.592 .538 .489 .445 .405
Discounted
Fuel Cost ADY 388 BS Be 292 265 241 219 199 181
Total Discounted Fuel Cost = $2,886
Maint. Cost 287 287 287 287 287 287 287 287 287 287
Discounted
Maint. Cost 274 249 226 ZUG 187 ile 154 140 Zs 116
Total Discounted Maintenance Cost = $1,850
Battery
Repl. Cost 2996 2996 2996 2996
Discounted
Battery Cost eco wo Ss EG Ae2 i323
Total Discounted Battery Cost = $7,259
Salvage Cost (735)
Discounted Salvage Cost (298)
Disc.
Yearly
mesmei. 12249 701 637 2940 527 2432 435 2007 359 1660 (1)
Discounted 10 Year Life Cycle Cost = $23,946
Discounted 8 Year Life Cycle Cost = (23,946/10) x 8 = $19,157
8 Year Life Cycle Vehicle Cost = (12249/10) x 8 = $9,799
8 Year Life cycle Fuel Cost = (2886/10) x 8 = $2,309
68
ELECTRICG=POWERED a ede ane:
LIFE CYCLE COST COMPUTATIONS S(eelianvEr,
8 Year Life Cycle Maint. Cost (incl. Batteries)
= ((1850 + 7259/10) 8 = Size
Discounted Alternative Life Cycle Cost —- Gai ie.
69
COMPRESSED NATURAL GAS-POWERED VEHICLE
PUR Ewe ce LESeOST <COMPUTATIONS
Year
Item 0 1 Z 3 4 5 6 7 8
Fixed
Invest. 49570
Vehicle
Invest. 9794
Fuel Cost 252 2 Ore AS 2 252 2512 ZO Zo 252
Discount
Factor ~954 -867 -788 ary mG 5 2 O92 S56 ~-489
biscounted
Fuel Cost 240 eS 199 181 164 149 136 ie
Total Discounted Fuel Cost = $1,410
Maintenance
Cost Ses S135 333 SoS 383 535 353 333
Discounted
Maint. Cost 318 289 262 239 247 197 179 163
Total Discounted Maintenance Cost = $1,864
Salvage Cost (317 )
Discounted Salvage Cost (400)
Discounted Unit
Yearly
Cashflows 9794 558 5107 461 420 381 346 Ba. C4)
Discounted Unit Life Cycle Cost = $12,668
Discounted Alternative Life Cycle Cost = 49,570 + 12,668x3
Note: Difference in unit life cycle cost from text is due to
rounding of numbers.
70
LO;
de
2
LS
14.
LIST OF -REEERENCES
"The Road Vehicle: Today and Tomorrow," Electric
Vehicles, V. 64, N- 27 -0une. 1972
Stuhlinger, Ernst, "Electric Automobiles--Ready for the
Market?" 18th Intersociety Energy Conversion
Engineering Conference, V. 3, 1983.
Noyes Data Corporation, Electric and Hybrid Vehicles,
lo 9.
Hamilton, William, Electric Automobiles, McGraw-Hill
BOOK “Company ,1960:
Unnewehr, eB. and Nasar, S cao Electric Vehicle
Technology, John Wiley & Sons, Inc., 1982.
Garrison, Clifton F. Jr., Decision Models for Conducting
an Economic Analysis of Alternative Fuels for the ICE
Engine, Ma S.M. Thesis, Naval Postgraduate School,
Monterey, California, March 1983.
Hamilton, William, "Costs of Electric Vehicles in Local
Fleet Service," 19th Intersociety of Energy Conversion
Engineering Conference, V. 2, 1984.
Telephone interview with Dr. Patil, U.S. Department of
Energy, Washington, D.C., 23 March 1987.
Watls, dic; "Compressed Natural Gas Could Replace
Gasoline as Vehicle Fuel of the Future," Pipeline & Gas
Journal, January 1986.
American Gas Association, Natural Gas Vehicles Market,
1936.
iS. Congress, Congressional Budget Office,
Understanding Natural Gas Price Decontrol, March 1983.
U.S. Department of Commerce, Statistical Abstract of the
United States 1986, Table No. 808.
American Gas Association, Rally for Fuel Savings, 1986.
American Data Association, Typical Questions and Answers
About Natural Gas Vehicles, 1986.
ene
ee
Gr
17a
Ss
1D"
ZO.
Zl
Ze «
Zor
24.
ZI.
ZO.
27].
28.
Davis, Margaret N., "An Examination of the Use of
Natural Gas Vehicles by Gas Utilities," Gas Energy
Review, V. 13, N. 5, May 1985.
American Gas Association, Cost Comparisons of Natural
Gas Vehicles Versus Gasoline-Fueled Vehicles Under
Various Refueling Options, 28 February, 1986.
Telephone interview with Dr. Jeffrey Seisler, American
Gas Association, Arlington, Virginia, 23 March 1987.
Department of Defense Instruction 7041.3, Economic
Analysis and Program Evaluation for Resource Management,
ikemoOectObelr 1972.
Blecke, Curtis J., Financial Analysis for Decision
Making, Prentice-Hall, Inc., 1966.
Boger, Dan, Presentation at Defense Logistics Agency
Workshop, "Alternative Vehicle Propulsion and the
Optimal Industrial Fleet," 6 December 1985.
Naval Postgraduate School Transportation Office, "1986
Usage Record," "1986 Budget/Expense Report."
Interviews with Ensign John Ehlert, Naval Postgraduate
School Transportation Officer, March 1987.
Driebeek, Norman J., Applied Linear Programming,
Addison-Wesley Publishing Co., 1969.
Lee, S.M., Moore, L.J. and Taylor, B.W., Management
Science, Wm. C. Brown Publishers, 1981.
Garfinkel, R.S. and Nemhauser, Gs Ls; Integer
Programming, John Wiley & Sons, 1972.
Boger, Dan, "Alternative Vehicle Propulsion and the
Optimal Industrial Fleet."
Interviews with Ensign John Ehlert, Naval Postgraduate
Ecce lransportaction Officer, April 1987.
Telephone interview with William Kummer, Texaco
Marketing Representative, Los Angeles, California, 6 May
oS 7/ .
72
INITIAL DISTRIBUTION hoe
No. Copies
Defense Technical Information Center 2
Cameron Station
Alexandria, Virginia 22304-6145
Library, Code 0142 2
Naval Postgraduate School
Monterey, California 93943-5002
Dr. Dan Boger, Code 54Bo 1
Naval Postgraduate School
Monterey, California 93943-5000
CDR Tim Sullivan, Code 55S] i
Naval Postgraduate School
Monterey, California 93943-5000
LT Danny Grenier 2
7016 Forest View Drive
Springfield, Virginia 22150
eS
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